This paper introduces the design and experiments of a gas tracking algorithm, named a circular movement algorithm, which is for natural indoor environment without a strong and constant wind. A graph of gas concentration shows tumultuous flow under the condition [8]. To solve the turbulent gas concentration problem, we defined cumulative-gas concentration (CGC) value to compute gradient of gas concentration and compare gas concentration values. Using the circular movement algorithm, the robot performs circular movement and collects gas concentration data to determine directions of gas source. The algorithm makes the robot able to track the directions of the gas source. This paper also introduces a tracking method using relative coordinate system for the tracking robot in the gas leaking circumstances which can calculate the location of the gas leakage without an absolute coordinate of a room or a building. As a result of experiments, the robot was able to detect a location of possible gas source by using the proposed circular movement algorithm and the relative coordinate system.